Option pricing with overnight and intraday volatility

• Published date: 01 November 2023
• Author: Fang Liang,Lingshan Du,Zhuo Huang
• Date: 01 November 2023
• DOI: http://doi.org/10.1002/fut.22448

Received: 3 February 2023

|

Accepted: 20 June 2023

DOI: 10.1002/fut.22448

RESEARCH ARTICLE

Option pricing with overnight and intraday volatility

Fang Liang

1,2

|Lingshan Du

3

|Zhuo Huang

4

1

International School of Business &

Finance, Sun Yat‐sen University,

Guangdong, China

2

Advanced Institute of Finance,

Sun Yat‐sen University, Guangdong,

China

3

Guanghua School of Management,

Peking University, Beijing, China

4

China Center for Economic Research,

National School of Development, Peking

University, Beijing, China

Correspondence

Zhuo Huang, China Center for Economic

Research, National School of

Development, Peking University, Beijing,

China.

Email: zhuohuang@nsd.pku.edu.cn

Funding information

National Natural Science Foundation of

China

Abstract

Efficiently exploiting the volatility information contained in price variations is

important for pricing options and other derivatives. In this study, we develop a

new and flexible option‐pricing model that explicitly specifies the joint

dynamics of overnight and intraday returns. The application of multivariate

Edgeworth–Sargan density enables us to derive analytical approximations for

option valuation formulas. Empirically, the model improves significantly upon

benchmark models using S&P 500 index options. In particular, its separate

modeling of intraday and overnight return volatility leads to an out‐of‐sample

gain of 7.24% in pricing accuracy compared with the modeling of the close‐to‐

close return volatility as a whole. The improvements are more pronounced

during highly volatile periods.

KEYWORDS

multivariate Edgeworth–Sargan density, option pricing, overnight volatility

JEL CLASSIFICATION

G13, C58, C51

1|INTRODUCTION

The proper specification of underlying asset volatility dynamics is a key element of an option valuation framework. A

growing body of literature advocates for the use of empirically grounded properties in option‐pricing models. These

studies use observed (realized) quantities to update volatility, such that volatility is no longer latent. This modeling

approach leads to more precise measurement and forecasting of asset volatility, and the theoretical and empirical

justifications for constructing reliable realized variance measures based on intraday high‐frequency observations are

given by Andersen, Bollerslev, Diebold, and Ebens et al. (2001), Andersen, Bollerslev, Diebold, and Labys (2001), and

Andersen et al. (2003), among others. Recent studies, such as Corsi et al. (2013), Christoffersen et al. (2014), and

Christoffersen et al. (2015), jointly model the dynamics of returns and realized variances under circumstances of option

pricing and verify that this type of option valuation model is superior to models optimized only on returns.

The aforementioned studies focus exclusively on total daily returns and do not distinguish information pertaining

to trading periods from that pertaining to nontrading periods. However, a halt in trading may result in a price

information process that differs from that resulting from continuous trading. As total daily (close‐to‐close) returns rely

only on the last tick price on an exchange for each trading day, close‐to‐close returns are not capable of effectively

reflecting news that arrives during market closure.

For instance, before opening, European investors submit orders based on information revealed in US stock markets,

and trading is performed at a single price that clears the market. This means that the opening price of the exchange

reflects accumulated overnight information from oversea markets (see, e.g., Chan et al., 1996; Taylor, 2007;

Tsiakas, 2008). Another strand of literature finds that extended futures trading (usually 24‐h‐trading, except on

J Futures Markets. 2023;43:1576–1614.wileyonlinelibrary.com/journal/fut1576

|

© 2023 Wiley Periodicals LLC.

weekends) contains information that is useful for explaining subsequent overnight spot returns. Hasbrouck (2003)

shows that S&P 500 E‐mini futures, which are traded overnight when the underlying stock market is closed, account

for approximately 90% of the movement of the S&P 500 index. Similarly, Craig et al. (1995) find close links between

implied changes and actual overnight changes in the Nikkei index. It is clear from both of the above strands of

literature that overnight information from overseas stock markets and futures markets is crucial for explaining

observed patterns in opening price reactions and unobserved patterns during nontrading periods.

Figure 1plots the averaged 1‐min returns and variances of the S&P 500 index from market open to close. It is not

surprising to find that the largest 1‐min variance for a trading day occurs when the market opens, as this variance

reflects the opening price reaction to information accumulated overnight from futures markets and overseas stock

markets. The figure shows that a standard U‐shaped pattern exists (Hong & Wang, 2000; Yang, 2022). The closing

variances, although tending to be higher than those earlier in the day, are not so dramatic as the opening variances.

Moreover, macroeconomic and corporate announcements released during nontrading hours can be predictive of

opening price, asset return, and volatility (see, e.g., Akey et al., 2022; Chan & Marsh, 2022; Hu et al., 2021; Jiang

et al., 2012). Moshirian et al. (2012) examine the impact of corporate news announcements released overnight on price

discovery during the preopening period in the Australian Securities Exchange and find that prices respond immediately

to overnight news upon the commencement of trading. Boudoukh et al. (2019) find that fundamental information in

firm‐level announcements accounts for 49.6% of overnight idiosyncratic volatility (vs. 12.4% of trading‐hour

idiosyncratic volatility). Furthermore, Atilgan (2014) obtains evidence that compared with volatility spreads on

nonearnings‐announcement days, volatility spreads on earnings‐announcement days

1

are more predictive of stock

returns.

To show the immediate reactions of asset returns and variances to overnight news releases, we consider the most

important US macroeconomic announcement, the nonfarm payroll employment release. The nonfarm payroll

employment is one of the most important announcements for all markets and it is often referred to as the “king”of

announcements by market participants (see, e.g., Andersen & Bollerslev, 1998; Andersen et al., 2007). Nonfarm payroll

employment is released at 8:30 Eastern Standard Time (EST) when the futures markets are open but the equity markets

FIGURE 1 Opening price reaction to accumulated overnight information. This figure presents the averaged 1‐min returns (left axis)

and 1‐min variances (right axis, variances are computed by 1‐min squared returns) of the S&P 500 index during trading hours. This sample

covers the period from July 2, 2003 to December 18, 2019.

1

Del Corral et al. (2003) find that nearly 93% of announcements are made during nontrading hours.

LIANG ET AL.

|

1577

are closed. Figure 2plots the averaged 1‐min returns and variances of the S&P 500 E‐mini futures in the period ranging

from 1 h before to 1 h after the announcement. As can be seen, there is a sharp increase in both returns and variances

immediately after the announcement, revealing an instantaneous market reaction to information incorporated into

overnight announcements. The variances from the announcement time to the market opening time are higher than

those before the announcement.

The effect of market closure on stock (index) returns has been considered extensively in the literature. For example,

weekend returns are lower than weekday returns (see, e.g., French, 1980; Gibbons & Hess, 1981; Keim &

Stambaugh, 1984). Moreover, returns over trading periods are more volatile than returns over nontrading periods (see,

e.g., Amihud & Mendelson, 1991; Fama, 1965; French & Roll, 1986; Oldfield & Rogalski, 1980). The aforementioned

studies examine the difference between the nature of overnight returns and that of intraday returns and have been

extended to incorporate overnight information to enhance the accuracy of volatility forecasting (see, e.g., Dhaene &

Wu, 2020; Linton & Wu, 2020; Tsiakas, 2008) and to manage risk within VaR models (Taylor, 2007).

However, few studies consider the influence of market closure on option pricing. Boes et al. (2007) model the

overnight change in the stock prices by a single jump in addition to a standard affine model that allows for stochastic

volatility and random jumps during the day, and find that both overnight and intraday jumps are important for option

pricing. Jones and Shemesh (2018) suggest that widespread and highly persistent option mispricing is driven by the

incorrect treatment of stock return variance during periods of market closure. Muravyev and Ni (2020) find a

remarkable day–night pattern: overnight average delta‐hedged option returns are negative, whereas intraday average

delta‐hedged option returns are slightly positive. Wang et al. (2022) integrate overnight returns, intraday returns, and

intraday realized volatility within an augmented autoregressive volatility model, in which overnight returns and

intraday returns are assumed to be independent.

Building on these insights, this study develops an option valuation model in which the underlying asset price

features specific overnight and intraday variance dynamics. Our modeling framework explicitly prices options with

distinct dynamics for overnight and intraday variations. To stress the difference in information, we use alternative

model‐free empirical measures driving overnight and intraday volatilities, respectively.

We find, for the SPX market over two separate periods, that both overnight and intraday volatilities are important

for option pricing. Our new proposed model, the Bisected Realized generalized autoregressive conditional

FIGURE 2 Instantaneous market reaction to information in overnight macroeconomic announcements. This figure presents the

averaged 1‐min returns and 1‐min variances (constructed by the square of 1‐min returns) of the S&P 500 E‐mini futures on days that the US

Bureau of Labor Statistics (BLS) announced the unemployment rate. The sample covers the period from July 2, 2003 to December 18, 2019.

Unemployment announcement dates are obtained from the website of the US BLS (http://www.bls.gov).

1578

|

LIANG ET AL.